Pairing in spin chains and spinless fermions with next-nearest neighbour interactions

TL;DR

This paper explores the complex phase diagrams of one-dimensional fermionic and spin chain models with extended interactions, revealing various phases including pairing-dominated regions, using analytical and numerical methods.

Contribution

It provides a comprehensive analysis of phase diagrams with next-nearest neighbour interactions, identifying new phases and transition lines, especially the cluster Luttinger liquids with pairing.

Findings

Identification of rich phase diagrams with multiple phases.

Discovery of transition lines with central charge c=3/2.

Emergence of exotic cluster Luttinger liquids with paired particles.

Abstract

We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest neighbour range. In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbour and next-nearest-neighbour interactions. Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations. The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles. In relation with recent studies, we show several emergent transition lines with a central charge $c = 3/2$ between the Luttinger-liquid and the cluster Luttinger liquid phases. These results could be experimentally investigated using highly-tunable quantum simulators.